%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:57:42 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t2_zfmisc_1,conjecture,
union(empty_set) = empty_set,
file('theBenchmark.p',t2_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_2_2,plain,
! [U_4] :
( ( U_4 = empty_set
| ? [U_3] : in(U_3,U_4) )
& ( ! [U_2] : ~ in(U_2,U_4)
| U_4 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_6] :
( U_6 = empty_set
| ? [U_3] : in(U_3,U_6) )
& ! [U_5] :
( ! [U_2] : ~ in(U_2,U_5)
| U_5 != empty_set ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_6] :
( U_6 = empty_set
| in(sK1(U_6),U_6) )
& ! [U_5] :
( ! [U_2] : ~ in(U_2,U_5)
| U_5 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_6))],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ in(U_2,U_5)
| U_5 != empty_set ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( U_6 = empty_set
| in(sK1(U_6),U_6) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_3_2,plain,
! [U_14,U_13] :
( ( U_13 = union(U_14)
| ? [U_12] :
( ( ~ in(U_12,U_13)
& ? [U_11] :
( in(U_11,U_14)
& in(U_12,U_11) ) )
| ( ! [U_10] :
( ~ in(U_10,U_14)
| ~ in(U_12,U_10) )
& in(U_12,U_13) ) ) )
& ( ! [U_9] :
( ( in(U_9,U_13)
| ! [U_8] :
( ~ in(U_8,U_14)
| ~ in(U_9,U_8) ) )
& ( ? [U_7] :
( in(U_7,U_14)
& in(U_9,U_7) )
| ~ in(U_9,U_13) ) )
| U_13 != union(U_14) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_22,U_20] :
( U_20 = union(U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] :
( in(U_11,U_22)
& in(U_18,U_11) ) )
| ? [U_17] :
( ! [U_10] :
( ~ in(U_10,U_22)
| ~ in(U_17,U_10) )
& in(U_17,U_20) ) )
& ! [U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(U_16,U_8) ) )
& ! [U_15] :
( ? [U_7] :
( in(U_7,U_21)
& in(U_15,U_7) )
| ~ in(U_15,U_19) ) )
| U_19 != union(U_21) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_22,U_20] :
( U_20 = union(U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] :
( in(U_11,U_22)
& in(U_18,U_11) ) )
| ? [U_17] :
( ! [U_10] :
( ~ in(U_10,U_22)
| ~ in(U_17,U_10) )
& in(U_17,U_20) ) )
& ! [U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(U_16,U_8) ) )
& ! [U_15] :
( ( in(sK2(U_21,U_19,U_15),U_21)
& in(U_15,sK2(U_21,U_19,U_15)) )
| ~ in(U_15,U_19) ) )
| U_19 != union(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2(U_21,U_19,U_15))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_22,U_20] :
( U_20 = union(U_22)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] :
( in(U_11,U_22)
& in(U_18,U_11) ) )
| ( ! [U_10] :
( ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10) )
& in(sK3(U_22,U_20),U_20) ) )
& ! [U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(U_16,U_8) ) )
& ! [U_15] :
( ( in(sK2(U_21,U_19,U_15),U_21)
& in(U_15,sK2(U_21,U_19,U_15)) )
| ~ in(U_15,U_19) ) )
| U_19 != union(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_22,U_20))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_22,U_20] :
( U_20 = union(U_22)
| ( ~ in(sK4(U_22,U_20),U_20)
& ? [U_11] :
( in(U_11,U_22)
& in(sK4(U_22,U_20),U_11) ) )
| ( ! [U_10] :
( ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10) )
& in(sK3(U_22,U_20),U_20) ) )
& ! [U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(U_16,U_8) ) )
& ! [U_15] :
( ( in(sK2(U_21,U_19,U_15),U_21)
& in(U_15,sK2(U_21,U_19,U_15)) )
| ~ in(U_15,U_19) ) )
| U_19 != union(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_18,sK4(U_22,U_20))],[f_3_5]) ).
fof(f_3_7,plain,
( ! [U_22,U_20] :
( U_20 = union(U_22)
| ( ~ in(sK4(U_22,U_20),U_20)
& in(sK5(U_22,U_20),U_22)
& in(sK4(U_22,U_20),sK5(U_22,U_20)) )
| ( ! [U_10] :
( ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10) )
& in(sK3(U_22,U_20),U_20) ) )
& ! [U_21,U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] :
( ~ in(U_8,U_21)
| ~ in(U_16,U_8) ) )
& ! [U_15] :
( ( in(sK2(U_21,U_19,U_15),U_21)
& in(U_15,sK2(U_21,U_19,U_15)) )
| ~ in(U_15,U_19) ) )
| U_19 != union(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5(U_22,U_20))],[f_3_6]) ).
cnf(f_3_8,plain,
( in(U_15,sK2(U_21,U_19,U_15))
| ~ in(U_15,U_19)
| U_19 != union(U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_9,plain,
( in(sK2(U_21,U_19,U_15),U_21)
| ~ in(U_15,U_19)
| U_19 != union(U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_10,plain,
( in(U_16,U_19)
| ~ in(U_8,U_21)
| ~ in(U_16,U_8)
| U_19 != union(U_21) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_11,plain,
( in(sK4(U_22,U_20),sK5(U_22,U_20))
| in(sK3(U_22,U_20),U_20)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_12,plain,
( in(sK5(U_22,U_20),U_22)
| in(sK3(U_22,U_20),U_20)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_13,plain,
( ~ in(sK4(U_22,U_20),U_20)
| in(sK3(U_22,U_20),U_20)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_14,plain,
( in(sK4(U_22,U_20),sK5(U_22,U_20))
| ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_15,plain,
( in(sK5(U_22,U_20),U_22)
| ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_16,plain,
( ~ in(sK4(U_22,U_20),U_20)
| ~ in(U_10,U_22)
| ~ in(sK3(U_22,U_20),U_10)
| U_20 = union(U_22) ),
inference(clausify,[status(thm)],[f_3_7]) ).
fof(f_4_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_4_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_5_2,plain,
? [U_23] : empty(U_23),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_23,sK6)],[f_5_2]) ).
cnf(f_5_4,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_6_2,plain,
? [U_24] : ~ empty(U_24),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_24,sK7)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,negated_conjecture,
union(empty_set) != empty_set,
inference(negate,[status(cth)],[t2_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
union(empty_set) != empty_set,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,negated_conjecture,
union(empty_set) != empty_set,
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:07:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------